The value of the integral \( \int_{0}^{2} \frac{\log \left(x^{2}+2\right)}{(x+2)^{2}} d x \) is ...

Описание

The value of the integral \( \int_{0}^{2} \frac{\log \left(x^{2}+2\right)}{(x+2)^{2}} d x \) is :
(a) \( \frac{\sqrt{2}}{3} \tan ^{-1} \sqrt{2}+\frac{5}{12} \log 2-\frac{1}{4} \log 3 \)
(b) \( \frac{\sqrt{2}}{3} \tan ^{-1} \sqrt{2}-\frac{5}{12} \log 2-\frac{1}{12} \log 3 \)
(c) \( \frac{\sqrt{2}}{3} \tan ^{-1} \sqrt{2}+\frac{5}{12} \log 2+\frac{1}{12} \log 3 \)
(d) \( \frac{\sqrt{2}}{3} \tan ^{-1} \sqrt{2}-\frac{5}{12} \log 2+\frac{1}{12} \log 3 \)
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